How do you test whether a measurement is perfectly precise? All real-world measurements have errors and imprecision, and every interval includes infinitely many numbers with finite representations and those with no finite representation in pretty much every nontrivial representation system. Our ability to distinguish between real-valued measurements is generally extremely poor in comparison with the density of numbers you can represent even in 64 bits, let alone the more than a trillion bits that might be employed in some hypothetical computer capable of simulating our universe.
Also note that many irrational numbers can be stored and exact arithmetic done on them within some bounded number of bits, though for any representation system there will always be numbers (including rational numbers!) that cannot. This doesn’t have real effect on your argument, but I thought that it might be useful to mention.
How do you test whether a measurement is perfectly precise? All real-world measurements have errors and imprecision, and every interval includes infinitely many numbers with finite representations and those with no finite representation in pretty much every nontrivial representation system. Our ability to distinguish between real-valued measurements is generally extremely poor in comparison with the density of numbers you can represent even in 64 bits, let alone the more than a trillion bits that might be employed in some hypothetical computer capable of simulating our universe.
Also note that many irrational numbers can be stored and exact arithmetic done on them within some bounded number of bits, though for any representation system there will always be numbers (including rational numbers!) that cannot. This doesn’t have real effect on your argument, but I thought that it might be useful to mention.